Chain rule formula and generalized mean value theorem for nabla fractional differentiation on time scale

Abstract

The nabla fractional derivative, which was introduced by Gogoi et.al., generalized the ordinary derivative with non-integer order, and unifies the continuous and discrete analysis using backward operator. In this study, we proposed a modification of their definition. The main focus of this work is to introduce a chain rule formula and a generalized mean value theorem for nabla fractional differentiation on time scale. Results of this study will be applied in finding the sum of a finite series.